Solve for x
x\in (-\infty,-1]\cup (4,\infty)
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x+1\leq 0 x-4<0
For the quotient to be ≥0, x+1 and x-4 have to be both ≤0 or both ≥0, and x-4 cannot be zero. Consider the case when x+1\leq 0 and x-4 is negative.
x\leq -1
The solution satisfying both inequalities is x\leq -1.
x+1\geq 0 x-4>0
Consider the case when x+1\geq 0 and x-4 is positive.
x>4
The solution satisfying both inequalities is x>4.
x\leq -1\text{; }x>4
The final solution is the union of the obtained solutions.
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